My Math Forum Plotting Supply & Demand Curve
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 August 7th, 2012, 08:43 PM #1 Newbie   Joined: Aug 2012 Posts: 10 Thanks: 0 Plotting Supply & Demand Curve Hey everyone, I'm new here, would love some help on this problem. *Note: At market equilibrium, we have Demand = Supply Code: The supply and demand functions for a good are given, respectively, by q = 2p + 10 , p(q + 4) = 60, where p is the price. a) Determine the equilibrium price and quantity, b) Sketch the supply and demand functions in the same graph for q?0. I've managed to solve part (a) but am having problems with part (b). (a) q = 2p + 10 -----(1) p(q + 4) = 60 ---(2) substitute (1) into (2) p ( (2p +10) + 4) = 60 2p^2 + 14p - 60 = 0 p^2 + 7p - 30 = 0 (p + 10) (p - 3) = 0 p = -10 or 3 But, price and quantity equilibrium can't be a negative, so p = 3. That's part (a) solved. Now I have no idea how to transition to part (b), help would be appreciated, thanks!
August 7th, 2012, 08:52 PM   #2
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Math Focus: Calculus/ODEs
Re: Plotting Supply & Demand Curve

Since this does not involve the calculus, I have moved the topic to the appropriate forum.

Here is a plot of the two functions on the same graph:

[attachment=0:2jyfbf79]supplydemand.jpg[/attachment:2jyfbf79]
Attached Images
 supplydemand.jpg (11.5 KB, 451 views)

 August 7th, 2012, 08:59 PM #3 Newbie   Joined: Aug 2012 Posts: 10 Thanks: 0 Re: Plotting Supply & Demand Curve How do you derive the coordinates in relation to the supply and demand equation? Given that we know the market equilibrium falls on the (3,16) coordinates.
 August 7th, 2012, 09:11 PM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Plotting Supply & Demand Curve If we let p be the independent variable, then the first equation: $q=2p+10$ is a line given in slope-intercept form. We know it will have the point (0,10) and since the slope is 2, it will also have the point (1,12). Then we just run a line through these two points. If we solve the second equation for q, we find: $q=\frac{60}{p}-4$ We see that this is a hyperbolic curve with vertical asymptote $p=0$ and horizontal asymptote $q=-4$. We also know it contains the point (3,16). It also has the p-intercept at (15,0). This is enough information to sketch the curve.
 August 7th, 2012, 09:24 PM #5 Newbie   Joined: Aug 2012 Posts: 10 Thanks: 0 Re: Plotting Supply & Demand Curve Thanks Mark. But what if I want p to be on the y-axis and q on the x-axis instead? And wouldn't the supply curve be: q = 2p +10 if q = 0, 0 = 2p+10 p = -5 (0 , -5) cutting through (16, 3) instead?
August 7th, 2012, 09:39 PM   #6
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Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,211
Thanks: 521

Math Focus: Calculus/ODEs
Re: Plotting Supply & Demand Curve

Yes, you would find the point (-5,0) to be on the line if we extend it to the left.

If we wish for q to be the independent variable instead, then we solve both equations for p:

(1) $p=\frac{q-10}{2}=\frac{q}{2}-5$

(2) $p=\frac{60}{q+4}$

[attachment=0:5pfdprrb]supplydemand2.jpg[/attachment:5pfdprrb]
Attached Images
 supplydemand2.jpg (10.0 KB, 447 views)

 August 7th, 2012, 09:51 PM #7 Newbie   Joined: Aug 2012 Posts: 10 Thanks: 0 Re: Plotting Supply & Demand Curve So, if I want to make a particular variable as the independent value, I'll just assume that it equals to 0? *ps: What kind of software are you using to input the equations and graphs on your answers? I noticed that it's not text based when I tried to highlight it.
 August 7th, 2012, 09:56 PM #8 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Plotting Supply & Demand Curve If you want a particular variable to be independent, then solve for the other variable. I am using the site http://www.wolframalpha.com/ to plot the graph. For the second graph I used the command: y=(x-10)/2,y=60/(x+4) for x = 0 to 20 Then, I hit [ALT][PRT SCRN] to save a screenshot to the clipboard, opened MS-Paint and copied, cropped and saved the image, then attached it.
 August 7th, 2012, 09:59 PM #9 Newbie   Joined: Aug 2012 Posts: 10 Thanks: 0 Re: Plotting Supply & Demand Curve Got it, thank you so much Mark! You've been a great help.
 August 7th, 2012, 10:02 PM #10 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Plotting Supply & Demand Curve Glad to help, and welcome to the forum!

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